In the FA Cup 64 teams play a knockout tournament. In the last
four years Arsenal have been drawn against Chelsea each year and
have beaten Chelsea every time. What is the probability of that
happening?
Let's say that whenever Arsenal and Chelsea play the
probability of Arsenal winning is 0.6 and otherwise, throughout
the tournament, both these teams have a probability of winning of
0.7 in the first round, 0.6 in the second round and 0.5 in the
subsequent rounds.